Proposition 2.1 (Proposition 1 of [1]}, lower bound on the minimax separation rate) 

Under (REF ), let \(H_{0, n}: \, q_n = 0\) 
and \(H_{1, n}\)  describe the setting where \(q_n= 2\) , \(d_n: = d_1 = -d_2\) 
and \(\delta _n: = \theta _2 - \theta _1\)  with \(n^{-1} \delta _n \rightarrow 0\) .
Then, \(H_{0, n}\)  and \(H_{1, n}\)  are asymptotically inseparable if
\(\vert d_n \vert \sqrt{\delta _n} \le \sqrt{2\log (n/\delta _n)} - \nu _n\) 
where \(\nu _n \rightarrow \infty \) .

